Arithmetic operands in C programming are fundamental to performing calculations and manipulating data. This article will explore the various aspects of arithmetic operands, focusing on their conversion rules and behaviors.
Boolean, Characters, and Integers
Every integer type in C has an integer conversion rank. This rank is used to determine the type of the result when different integer types are used in an operation. The rank is defined as follows:
- No two signed integer types shall have the same rank, even if they have the same representation.
- The rank of a signed integer type shall be greater than the rank of any signed integer type with less precision.
- The rank of `long long int` shall be greater than the rank of `long int`, which shall be greater than the rank of `int`, which shall be greater than the rank of `short int`, which shall be greater than the rank of `signed char`.
- The rank of any unsigned integer type shall equal the rank of the corresponding signed integer type, if any.
- The rank of any standard integer type shall be greater than the rank of any extended integer type with the same width.
- The rank of `char` shall equal the rank of `signed char` and `unsigned char`.
- The rank of `_Bool` shall be less than the rank of all other standard integer types.
- The rank of any enumerated type shall equal the rank of the compatible integer type.
- The rank of any extended signed integer type relative to another extended signed integer type with the same precision is implementation-defined, but still subject to the other rules for determining the integer conversion rank.
The following may be used in an expression wherever an `int` or `unsigned int` may be used:
- An object or expression with an integer type (other than `int` or `unsigned int`) whose integer conversion rank is less than or equal to the rank of `int` and `unsigned int`.
- A bit-field of type `_Bool`, `int`, `signed int`, or `unsigned int`.
If an `int` can represent all values of the original type (as restricted by the width, for a bit-field), the value is converted to an `int`; otherwise, it is converted to an `unsigned int`. These are called the integer promotions. All other types are unchanged by the integer promotions.
The integer promotions preserve value including sign. Whether a “plain” `char` can hold negative values is implementation-defined.
Boolean Type
When any scalar value is converted to `_Bool`, the result is `0` if the value compares equal to `0`; otherwise, the result is `1`.
Signed and Unsigned Integers
When a value with integer type is converted to another integer type other than `_Bool`, if the value can be represented by the new type, it is unchanged. Otherwise, if the new type is unsigned, the value is converted by repeatedly adding or subtracting one more than the maximum value that can be represented in the new type until the value is in the range of the new type. If the new type is signed and the value cannot be represented in it, either the result is implementation-defined or an implementation-defined signal is raised.
Real Floating and Integer
When a finite value of real floating type is converted to an integer type other than `_Bool`, the fractional part is discarded (i.e., the value is truncated toward zero). If the value of the integral part cannot be represented by the integer type, the behavior is undefined.
When a value of integer type is converted to a real floating type, if the value being converted can be represented exactly in the new type, it is unchanged. If the value being converted is in the range of values that can be represented but cannot be represented exactly, the result is either the nearest higher or nearest lower representable value, chosen in an implementation-defined manner. If the value being converted is outside the range of values that can be represented, the behavior is undefined.
Real Floating Types
When a value of real floating type is converted to a real floating type, if the value being converted can be represented exactly in the new type, it is unchanged. If the value being converted is in the range of values that can be represented but cannot be represented exactly, the result is either the nearest higher or nearest lower representable value, chosen in an implementation-defined manner. If the value being converted is outside the range of values that can be represented, the behavior is undefined.
Complex Types
When a value of complex type is converted to another complex type, both the real and imaginary parts follow the conversion rules for the corresponding real types.
Real and Complex
When a value of real type is converted to a complex type, the real part of the complex result value is determined by the rules of conversion to the corresponding real type and the imaginary part of the complex result value is a positive zero or an unsigned zero.
When a value of complex type is converted to a real type other than `_Bool`, the imaginary part of the complex value is discarded and the value of the real part is converted according to the conversion rules for the corresponding real type.
Usual Arithmetic Conversions
Many operators that expect operands of arithmetic type cause conversions and yield result types in a similar way. The purpose is to determine a common real type for the operands and result. For the specified operands, each operand is converted, without change of type domain, to a type whose corresponding real type is the common real type. Unless explicitly stated otherwise, the common real type is also the corresponding real type of the result, whose type domain is the type domain of the operands if they are the same, and complex otherwise. This pattern is called the usual arithmetic conversions.
The values of floating operands and of the results of floating expressions may be represented in greater range and precision than that required by the type; the types are not changed thereby.
